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Which is the greatest number in the following set?

[tex]\[ -6 \frac{2}{3}, \, -6.6, \, -6.06, \, -6 \frac{2}{5} \][/tex]

A. [tex]\[ -6 \frac{2}{3} \][/tex]

B. -6.6

C. -6.06

D. [tex]\[ -6 \frac{2}{5} \][/tex]


Sagot :

Let's determine which number in the set [tex]\(-6 \frac{2}{3}, -6.6, -6.06, -6 \frac{2}{5}\)[/tex] is the greatest.

Step 1: Convert each fraction to its decimal form

1. Convert [tex]\(-6 \frac{2}{3}\)[/tex]:

[tex]\[ -6 \frac{2}{3} = -6 - \frac{2}{3} = -6 - 0.6667 = -6.6667 \][/tex]

2. Convert [tex]\(-6 \frac{2}{5}\)[/tex]:

[tex]\[ -6 \frac{2}{5} = -6 - \frac{2}{5} = -6 - 0.4 = -6.4 \][/tex]

The set now consists of the following decimals:
[tex]\[ -6.6667, -6.6, -6.06, -6.4 \][/tex]

Step 2: Compare the decimal values

Let's list them in ascending order (since we are looking for the greatest number, it helps to see them organized this way):

1. [tex]\(-6.6667\)[/tex]
2. [tex]\(-6.6\)[/tex]
3. [tex]\(-6.4\)[/tex]
4. [tex]\(-6.06\)[/tex]

Clearly, [tex]\(-6.06\)[/tex] is the largest value as it is less negative than the other numbers.

Conclusion:

The greatest number in the set is [tex]\( \boxed{-6.06} \)[/tex].
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